Since the investigators are looking for the highest one-time dose of the anti-inflammatory donor cells that can be administered safely in combination with IL-2 without severe or unmanageable side effects in participants that have cGVHD, not everyone who participates in this research study will receive the same dose of the donor cells. The cell dose you get will depend on the number of participants who have been enrolled in the study before you and how well they have tolerated their cell doses.